LOCALIZATION (Mathematics)Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module of dimension d. For each i ∈ N0 let HI,Ji (-) denote the i-th right derived functor of ΓI,J (-), where ΓI,J (M) := {x ∈ M : Inx Jx for n 1}. If R ...
(The proof is a straightforward modification, to the ease of A-primes, of an argument concerning the behaviour of prime ideals under localization.) (b) We begin by noticing that Pa : Gama (B) ~ Spee (A) is a continuous and spec- tral map. As a matter of a fact, ~Ais the ~,...
TY - JOURAU - Ratcliff, Louis J., Jr.TI - Note on Asymptotic Prime Divisors and Symbolic Powers of Primary Ideals.JO - Mathematische ZeitschriftPY - 1983VL - 184SP - 417EP - 424LA - engKW - asymptotic prime divisors; symbolic powers; Noetherian ring; powers of primary ideal; Cohen-Mac...
If P is an almost complete intersection, then P (i) =P i for all i if and only if A (Q) , the ring of homogeneous elements of degree 0 in A Q , is a complete intersection for all ht1 homogeneous prime ideals Q of A. The similarity between the two results rests on the ...
Let R be a maximal order and A, B be R-ideals of R. Clearly (A B)* superset of B*A* is satisfied and if R is a Dedekind prime ring, the equality holds, i.e., (AB)* = B*A*. However, the equality is not true in general. In this paper, we answer the question: If R ...
In this paper, we investigate relationships between different definitions of fuzzy ideals of a fuzzy semigroup. The equivalence of different definitions of fuzzy ideals of a fuzzy semigroup is obtained. We show that the lattice of all phi-fuzzy ideals of a fuzzy semigroup X is a complete sub...
Johnny had high-minded ideals when he founded the club in the 1960s. Over the course of the next decade, Johnny and his friends are almost unrecognizable in what they’re willing to do for the club. Despite Benny’s love for Kathy, he keeps getting drawn back into Johnny’s vision for...
Prime Ideals and LocalizationThis chapter summarizes standard results in commutative algebra. For more details, see [Bour], Chap. II, III, IV.doi:10.1007/978-3-662-04203-8_1SerreJean-PierreSpringer Berlin Heidelberg
In this paper we present a technical lemma about localization at countably infinitely many prime ideals. We apply this lemma to get many results about the finiteness of associated prime ideals of local cohomology modules.doi:10.1142/S0219498816500456Kamal Bahmanpour...
Journal of AlgebraJ.W. Brewer, D.L. Costa, E.L. Lady, Prime ideals and localization in commutative group rings, Journ. of Algebra 34 (1975), 300-308.J. W. Brewer, D. L. Coasta and E. L. Lady, Prime ideals and localization in commuta- tive group rings, J. Algebra, 34 (...